Arf numerical semigroups with low multiplicity via Grobner basis

In this paper, the Grobner basis over RF-matrices of Arf numerical semigroups are presented. The Arf properties ideals for the RF-matrices obtained by RF-Relations are provided and the aforementioned concepts are associated through the Grobner basis of the Arf numerical semigroup. Moreover, we prove that if we have a minimal presentation (or a Grobner basis of the ideal associated to the semigroup), then this will be a system of generators of the subgroup of Z(p) with the equation n(1)x(1) + n(2)x(2) + center dot center dot center dot+ n(p)x(p) = 0, where {n(1), n(2), ... , n(p)} are the generators of numerical semigroup G.